Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D61 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#459 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #459 | D61 |
| hypocenter | C61 | #3106 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840310 | C2 | semidirect |
| 2. C4×#11758224 | C2 | semidirect |
| 3. #16840084 | C2 | semidirect |
| 4. #16840058 | C2 | semidirect |
| 5. #16840052 | C2 | semidirect |
| 6. #16839959 | C2 | semidirect |
| 7. #16839904 | C2 | semidirect |
| 8. #16839853 | C2 | semidirect |
| 9. D8×Dic61 | C2 | semidirect |
| 10. #16839814 | C2 | semidirect |
| 11. C61×#459 | C2 | semidirect |
| 91. D4×C61 | #41 | semidirect |
| 114. Dic122 | #41 | semidirect |
| 151. #459 | D61 | semidirect |
| 156. C61 | #3106 | semidirect |
| 241. D4 | #11758224 | semidirect |